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Resolución de integrales/ x^2+4/ sin(x^2+4)

Integral de sin(x^2+4) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1               
  /               
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 |     / 2    \   
 |  sin\x  + 4/ dx
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/                 
0
∫01sin⁡(x2+4) dx\int\limits_{0}^{1} \sin{\left(x^{2} + 4 \right)}\, dx 
Integral(sin(x^2 + 4), (x, 0, 1))
Solución detallada

    FresnelSRule(a=1, b=0, c=4, context=sin(x**2 + 4), symbol=x)

  1. Añadimos la constante de integración:

    2π(sin⁡(4)C(2xπ)+cos⁡(4)S(2xπ))2+constant\frac{\sqrt{2} \sqrt{\pi} \left(\sin{\left(4 \right)} C\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right) + \cos{\left(4 \right)} S\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right)\right)}{2}+ \mathrm{constant}

Respuesta:

2π(sin⁡(4)C(2xπ)+cos⁡(4)S(2xπ))2+constant\frac{\sqrt{2} \sqrt{\pi} \left(\sin{\left(4 \right)} C\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right) + \cos{\left(4 \right)} S\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right)\right)}{2}+ \mathrm{constant}

Respuesta (Indefinida) [src] 
                                     /        /    ___\    /    ___\       \
                          ___   ____ |        |x*\/ 2 |    |x*\/ 2 |       |
  /                     \/ 2 *\/ pi *|cos(4)*S|-------| + C|-------|*sin(4)|
 |                                   |        |   ____|    |   ____|       |
 |    / 2    \                       \        \ \/ pi /    \ \/ pi /       /
 | sin\x  + 4/ dx = C + ----------------------------------------------------
 |                                               2                          
/
∫sin⁡(x2+4) dx=C+2π(sin⁡(4)C(2xπ)+cos⁡(4)S(2xπ))2\int \sin{\left(x^{2} + 4 \right)}\, dx = C + \frac{\sqrt{2} \sqrt{\pi} \left(\sin{\left(4 \right)} C\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right) + \cos{\left(4 \right)} S\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right)\right)}{2}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.901-2
Trazar el gráfico f(x)
Respuesta [src] 
             /        /  ___ \    /  ___ \       \
  ___   ____ |        |\/ 2  |    |\/ 2  |       |
\/ 2 *\/ pi *|cos(4)*S|------| + C|------|*sin(4)|
             |        |  ____|    |  ____|       |
             \        \\/ pi /    \\/ pi /       /
--------------------------------------------------
                        2
2π(sin⁡(4)C(2π)+cos⁡(4)S(2π))2\frac{\sqrt{2} \sqrt{\pi} \left(\sin{\left(4 \right)} C\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) + \cos{\left(4 \right)} S\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right)\right)}{2} 
=
= 
             /        /  ___ \    /  ___ \       \
  ___   ____ |        |\/ 2  |    |\/ 2  |       |
\/ 2 *\/ pi *|cos(4)*S|------| + C|------|*sin(4)|
             |        |  ____|    |  ____|       |
             \        \\/ pi /    \\/ pi /       /
--------------------------------------------------
                        2
2π(sin⁡(4)C(2π)+cos⁡(4)S(2π))2\frac{\sqrt{2} \sqrt{\pi} \left(\sin{\left(4 \right)} C\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) + \cos{\left(4 \right)} S\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right)\right)}{2} 
sqrt(2)*sqrt(pi)*(cos(4)*fresnels(sqrt(2)/sqrt(pi)) + fresnelc(sqrt(2)/sqrt(pi))*sin(4))/2
Respuesta numérica [src] 
-0.887351096487103
-0.887351096487103

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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